Gene regulatory networks that operate in the dynamically critical regime (between order and chaos) are optimised with respect to the trade-off between phenotypic robustness and flexibility — a balance that ensures both homeostasis and development. In fact, analyses of the gene network architecture and patterns of transcriptome changes in several organisms in the past few years suggest that the gene regulatory networks of living organisms are indeed in the critical regime. But how does a gene regulatory network evolve a structure that confers criticality? While this question has evaded scientists for decades, a related equally fundamental question has over the past years attracted considerable interesy: the evolution of evolvability. There is now the consensus that evolvability itself is a selectable trait. Evolvability, similar to criticality, is associated with the trade-off between mutational robustness on the one hand (mutations should not disrupt essential functions) and innovation on the other hand (mutations should alter networks sufficiently to add new functions). In this work I will show that critical dynamics in genetic network models naturally emerge as a robust byproduct of the very same evolutionary processes that select for evolvability — without fine-tuning of parameters or imposing explicit selection criteria (i.e. arbitrary fitness functions). More specificaly, criticality emerges from the requirement of evolvability in the sense that during evolution, the existing adaptive phenotypes must be preserved while allowing new phenotypes to emerge for the organism to be able to cope with new environmental challenges. Strikingly, the gene networks produced by selecting for evolvability have a structure (topology) that is very similar to the one observed in real organisms, such as Escherichia col, characterized by the existence of global regulators.